Collision frequencies across collision regimes in two-component systems

Agglomeration is the most important growth process in particle systems but modelling efforts typically assume mono-disperse primary particle distributions for the closure of the collision frequency that determines the growth rates. Real systems such as sooting flames, however, involve poly-disperse primary particle distributions. Also, systems with multiple components, where primary particles are of distinct but different sizes, cannot be treated as mono-disperse. Here, we introduce bi-disperse primary particle distributions and use Langevin dynamics simulations to develop closures for the collision kernels that are applicable over a wide range of agglomerate characteristics. The simulations cover fractal dimensions from 1.4 to 2.2, primary particle diameters from 5 nm to 50 nm, primary particle size ratios from 2 to 10 and agglomerates of up to a size of 200 primary particles with varying particle compositions. The Langevin dynamics simulations cover all collision regimes from ballistic to diffusive and allow to deduce expressions for the respective collision diameters, the hydrodynamic radii and the projected area as functions of particle characteristics. It is shown that existing expressions for the transition regime that were developed for the modelling of the collision kernel of spherical particles continue to hold for collision kernels of agglomerates in two-component systems under the condition that the collision diameters and drag coefficients are modelled accurately. An example ‘a posteriori’ simulation for a particle size ratio of 6 uses the population balance equation and demonstrates that bi-variate kernels are needed for the accurate prediction of the growth rates. Errors in predicted number density at the end of the simulations are less than 12 % while mono-variate kernels developed for mono-disperse primary particle systems overpredict the growth rate by 46%.